\section{Conclusion}
\label{sec:conclusion}

The locELM reproduction delivers a faithful modular implementation of the methodology outlined by Dong and Li, complete with documentation, examples, and diagnostic tooling. Empirical tests confirm that the solver captures the qualitative benefits of domain-local extreme learning machines, yet the quantitative mismatch in one dimension and the severe performance overhead in two dimensions prevent full replication of the published benchmarks.

Resolving these discrepancies hinges on uncovering subtle implementation details and optimising the automatic differentiation workflow. With the proposed corrective actions in place, the project is well positioned to achieve reproducible accuracy and to extend the framework to more demanding PDE scenarios.
